Shawn Kenny, Ph.D., P.Eng. Assistant Professor Faculty of Engineering and Applied Science Memorial University of Newfoundland ENGI 1313 Mechanics I Lecture 24:2-D Rigid Body Equilibrium

ENGI 1313 Statics I – Lecture 24© 2007 S. Kenny, Ph.D., P.Eng. 2 Mid-Term Examination Try to return by end of next week Will provide hand worked solution Can review once you receive the mid-term results Pencil case and water bottle left in 1040

ENGI 1313 Statics I – Lecture 24© 2007 S. Kenny, Ph.D., P.Eng. 3 General Announcement Allergies  Appreciated if you can refrain from wearing or using scented products

ENGI 1313 Statics I – Lecture 24© 2007 S. Kenny, Ph.D., P.Eng. 4 Lecture 24 Objective to understand concept of two-force and three-force member to illustrate application of 2D equations of equilibrium for a rigid body

ENGI 1313 Statics I – Lecture 24© 2007 S. Kenny, Ph.D., P.Eng. 5 Two-Force Member Conditions  No couple forces or couple moments  Neglect self-weight  Collinear forces

ENGI 1313 Statics I – Lecture 24© 2007 S. Kenny, Ph.D., P.Eng. 6 Two-Force Member (cont.) What is the Motivation to Recognize that a Rigid Body is a Two Force Member?

ENGI 1313 Statics I – Lecture 24© 2007 S. Kenny, Ph.D., P.Eng. 7 Two-Force Member (cont.) Motivation?  Simplify equilibrium analysis

ENGI 1313 Statics I – Lecture 24© 2007 S. Kenny, Ph.D., P.Eng. 8 Three-Force Member Conditions  Concurrent force system  Parallel force system

ENGI 1313 Statics I – Lecture 24© 2007 S. Kenny, Ph.D., P.Eng. 9 Comprehension Quiz The three scalar equations  F x =  F y =  M o = 0, are ____ equations of equilibrium in 2-D.  A) incorrect  B) the only correct  C) the most commonly used  D) not sufficient Answer: C Alternative Equilibrium Equations

ENGI 1313 Statics I – Lecture 24© 2007 S. Kenny, Ph.D., P.Eng. 10 Statically Determinate Structure 1. Determine Number of Reaction Forces or Unknowns 2. Determine Number of Equilibrium Equations Available 3. Evaluate  # Equations  # Unknowns  Linear system of equations solved

ENGI 1313 Statics I – Lecture 24© 2007 S. Kenny, Ph.D., P.Eng. 11 Statically Determinate Structure (cont.) F AxAx AyAy ByBy AB What are the Support Reactions? What are the Equilibrium Equations? y x

ENGI 1313 Statics I – Lecture 24© 2007 S. Kenny, Ph.D., P.Eng. 12 Statically Indeterminate Structure F AxAx AyAy ByBy AB What are the Support Reactions? What are the Equilibrium Equations? y x CyCy C

ENGI 1313 Statics I – Lecture 24© 2007 S. Kenny, Ph.D., P.Eng. 13 Solving 2-D Equilibrium 1. X-Y Coordinate System  Establish suitable right, rectangular coordinate system if not provided

ENGI 1313 Statics I – Lecture 24© 2007 S. Kenny, Ph.D., P.Eng. 14 Solving 2-D Equilibrium (cont.) Establish Suitable Coordinate System  Key Decision Factors? Relative orientation of the applied loads and rigid body (structure) Simplest or most direct resolution of force components

ENGI 1313 Statics I – Lecture 24© 2007 S. Kenny, Ph.D., P.Eng. 15 Solving 2-D Equilibrium (cont.) Example Suitable Coordinate System

ENGI 1313 Statics I – Lecture 24© 2007 S. Kenny, Ph.D., P.Eng. 16 Solving 2-D Equilibrium (cont.) 2. Draw the Rigid Body Free Body Diagram (FBD) Drill Rig Idealized Model Rigid Body FBD

ENGI 1313 Statics I – Lecture 24© 2007 S. Kenny, Ph.D., P.Eng. 17 Solving 2-D Equilibrium (cont.) 3. Apply the Appropriate Equilibrium Equations Alternative Equilibrium Equations

ENGI 1313 Statics I – Lecture 24© 2007 S. Kenny, Ph.D., P.Eng. 18 Important Considerations Order of Application for Equations of Equilibrium What are the Support Reactions?

ENGI 1313 Statics I – Lecture 24© 2007 S. Kenny, Ph.D., P.Eng. 19 Important Considerations (cont.) Order of Application for Equations of Equilibrium What is the first equilibrium equation to use? Why?

ENGI 1313 Statics I – Lecture 24© 2007 S. Kenny, Ph.D., P.Eng. 20 Important Considerations (cont.) Negative Scalar Solutions to Equilibrium Equations?  Force or couple moment opposite to that assumed in the FBD for the designated convention y x AyAy

ENGI 1313 Statics I – Lecture 24© 2007 S. Kenny, Ph.D., P.Eng. 21 Comprehension Quiz Which equation of equilibrium allows you to determine the force F immediately?  A)  F x = 0  B)  F y = 0  C)  M A = 0  D) Any one of the above. Answer: C 100 N AxAx AyAy A y x F 

ENGI 1313 Statics I – Lecture 24© 2007 S. Kenny, Ph.D., P.Eng. 22 Example The lever ABC is pin- supported at A and connected to a short link BD as shown. If the weight of the members is negligible, determine the force of the pin on the lever at A.

ENGI 1313 Statics I – Lecture 24© 2007 S. Kenny, Ph.D., P.Eng. 23 Example (cont.) What Key Features of the Problem Can Be Recognized?  Bracket or link BD is a two-force member  Lever ABC is a three- force member

ENGI 1313 Statics I – Lecture 24© 2007 S. Kenny, Ph.D., P.Eng. 24 Example (cont.)

ENGI 1313 Statics I – Lecture 24© 2007 S. Kenny, Ph.D., P.Eng. 25 Example (cont.)

ENGI 1313 Statics I – Lecture 24© 2007 S. Kenny, Ph.D., P.Eng. 26 Example (cont.)

ENGI 1313 Statics I – Lecture 24© 2007 S. Kenny, Ph.D., P.Eng. 27 Example (cont.) Concurrent Forces

ENGI 1313 Statics I – Lecture 24© 2007 S. Kenny, Ph.D., P.Eng. 28 Example (cont.)

ENGI 1313 Statics I – Lecture 24© 2007 S. Kenny, Ph.D., P.Eng. 29 References Hibbeler (2007) mech_1